A Mathematical Model to Utilize the Logistic Function in Germination and Seedling Growth

Abstract

Several models have been proposed to describe germination rates, but most are limited in statistical analysis and biological meaning of indices. Therefore, a mathematical model is proposed to utilize the logistic function. The function was defined as an overall response including time, temperature, and the interaction between time and temperature. Cumulative germination percentages over time were used to develop the model. Germination tests were conducted on indiangrass (Sorghastrum nutans (L.) Nash) strain ‘IG-2C-F1’, at constant temperatures of 9, 12, 15, 20, 25, and 30 °C. The function fitted the observed data over six temperatures at r² = 0.99. Time to reach 10% of final germination (Gt₁₀) increased from 2.5 d at 30 °C to 44.0 d at 9 °C, and Gt₅₀ (time to reach 50% of final germination) increased from 3.6 d at 30 °C to 53.8 d at 9 °C. True germination rate (% d⁻¹) for each temperature was maximum at Gt₅₀. A linear model of 1/Gt₅₀ versus temperature was used to estimate the base temperature of 8.3 °C for germination. An Arrhenius plot indicated a change occurred between 20 °C and 25 °C for temperature response of germination. Published data on hypocotyl growth of Cucumis melo L. were recalculated using the model. Absolute growth rates showed a temperature response similar to the published weighted-mean elongation rates. Base temperature for hypocotyl growth of C. melo was estimated as 8.8 °C. The proposed model proved to be useful in calculating and interpreting germination and growth kinetics.